Locating sensor nodes through correlations

ABSTRACT

A method is provided for estimating distances between sensor nodes. The method includes receiving a temporal sequence of measurements of a selected local environmental condition from each of the sensor nodes. The method includes determining an amount of correlation between the measurements of the selected local environmental condition that were received from two or more of the sensor nodes. The method also includes estimating distances between the two or more of the sensor nodes based on the determined amount of correlation.

CROSS REFERENCE TO RELATED APPLICATION

This application is a Divisional of U.S. application Ser. No.11/285,873, filed on Nov. 23, 2005 now U.S. Pat. No. 8,140,261, to YuliyBaryshnikov entitled “LOCATING-SENSOR NODES THROUGH CORRELATIONS,”currently allowed; commonly assigned with the present invention andincorporated herein by reference.

FIELD OF THE INVENTION

The invention relates generally to sensor nodes and methods foroperating distributed collections of sensor nodes.

DISCUSSION OF THE RELATED ART

This section introduces various related aspects of the art, which mayfacilitate a better understanding of aspects of the present invention.While the statements are explanatory, they should not be understood tobe admissions of prior art.

It is often desirable to know the spatial locations of the nodes of anetwork. The spatial locations may, e.g., be determined by directlymeasuring the distances of the nodes from fixed spatial markers. Suchdistance measurements may be made physically, e.g., with tape measures,or may be made indirectly with satellite global positioning system(GPS). In either method, the determination of the spatial locations eachnode of the network may be costly, because the measurements involveeither costly human intervention or costly equipment, e.g., multiple GPStransponders.

To reduce expenses, alternate methods have been proposed for determiningthe spatial locations of the nodes of networks. The alternate methodsare almost coordinate-free, because they rely primarily on determiningrelative locations of node pairs. From the relative locations, absolutespatial locations of the nodes may be determined by combining themeasured relative locations with the measurement of the absolutelocations of one or a few nodes. For example, determination of absolutelocations of the nodes of a network may involve using GPS transpondersto determine the absolute spatial locations of one or a few nodes ratherthan using a GPS transponder to determine the absolute spatial locationof each node of the network.

One such alternate method for spatially locating the nodes of a networkuses direct communications between node-pairs. According to this method,pairs of nodes communicate directly with each other, i.e., withoutretransmission via third nodes. Herein, these direct inter-nodecommunications are referred to as “inter-node chatter”. Duringinter-node chatter, one node of a pair transmits, e.g., a signal havinga known strength or a known transmission time, and the other node of thepair measures, e.g., the strength of the signal or the arrival time ofthe signal. From such strength and/or arrival time measurements, thereceiving node estimates the attenuation of the signal or thetransmission delay of the signal. By comparing the attenuation ortransmission delay for inter-node chatter from different transmittingnodes, a receiving node estimates the relative distances of saidtransmitting nodes, e.g., to determine which transmitting node or nodesare closest.

While this alternate method may enable determinations of relativespatial locations of nodes, methods based on inter-node chatter areoften undesirable. Indeed, some types of sensor nodes do not exchangesignals with each other and are commonly known as anchorite sensors. Inlarge sensor arrays, e.g., arrays having 10⁵-10⁷ sensor nodes, anchoritesensors can provide important advantages. In particular, in large sensorarrays, equipping individual nodes to support inter-node chatter wouldbe significantly more costly than making the nodes anchoritic. Thus, thefactor of cost may make inter-node chatter an undesirable tool for usein determining the spatial locations of individual nodes.

BRIEF SUMMARY

Certain aspects commensurate in scope with the disclosed embodiments arecollection forth below. It should be understood that these aspects arepresented merely to provide the reader with a brief summary of someembodiments and that these aspects are not intended to limit the scopeof the claims. The invention may however, encompass a variety of aspectsthat may not be collected below.

In one embodiment, a method is provided for estimating distances betweensensor nodes. The method includes receiving a temporal sequence ofmeasurements of a selected local environmental condition from each ofthe sensor nodes. The method includes determining an amount ofcorrelation between the measurements of the selected local environmentalcondition that were received from two or more of the sensor nodes. Themethod also includes estimating distances between the two or more of thesensor nodes based on the determined amount of correlation.

In another embodiment, a data storage medium is provided. The mediumencodes a machine-executable or digital processor-executable program.The program includes a sequence of instructions for performing a method.The method includes receiving a plurality of temporal sequences ofmeasurements of a selected local environmental condition. Acorresponding sensor node makes each of the sequences of measurements.The method includes determining an amount of correlation between thesequences of measurements of the selected local environmental conditionreceived from two or more of the sensor nodes. The method also includesestimating distances between the two or more of the sensor nodes basedon the determined amount of correlation.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a top view that schematically illustrates an exemplaryspatially distributed collection of sensor nodes;

FIG. 2 illustrates a data structure that some embodiments of theindividual sensor nodes of FIG. 1 maintain;

FIG. 3 is a flow chart illustrating a method for estimating pair wisedistances between sensor nodes, e.g., the sensor nodes of the collectionin FIG. 1;

FIG. 4A-4C illustrate how a cloud shadow may move over a collection ofsensor nodes in an embodiment of the method of FIG. 3 where each sensornode measures a local binary variable for the presence or absence of acloud shadow; and

FIG. 5 illustrates how a cloud shadow may move along a different pathover the collection of sensor nodes in the same embodiment illustratedin FIGS. 4A-4C;

FIG. 6 illustrates how a cloud shadow of a different size may move alonga another path over the collection of sensor nodes in the sameembodiment illustrated in FIGS. 4A-4C;

FIG. 7A plots magnitudes of 2-point cumulants that were simulated forround clouds in an embodiment of the method of FIG. 3 where the sensornodes measure a local variable for the presence or absence of a cloudshadow;

FIG. 7B plots magnitudes of 2-point cumulants that were simulated for½-plane clouds in an embodiment of the method of FIG. 3 where the sensornodes measure a variable for the presence or absence of a cloud shadow;

FIG. 8 is a flow chart illustrating a method for mapping the locationsof the sensor nodes of a collection, e.g., the sensor nodes of FIG. 1;and

FIG. 9 schematically illustrates a hardware device for performing themethod of FIG. 3 and/or the method of FIG. 8.

Various embodiments are described more fully by the Figures and DetailedDescription of Illustrative Embodiments. The inventions may, however, beembodied in various forms and are not limited to embodiments describedin the Figures and Detailed Description of Illustrative Embodiments.

In the Figures and Detailed Description of the Illustrative Embodiments,like reference numerals indicate elements with similar functions.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Various embodiments estimate pair wise distances between sensor nodes bydetermining spatial correlations between local measurements of one ormore environmental conditions by different ones of the sensor nodes.Since the local values of the one or more environmental conditions canchange in time, spatial correlations between the values measured by apair of sensor nodes can provide a measure of the spatial separationbetween the sensor nodes. Using such spatial correlations enablesreducing or eliminating reliance on inter-node chatter for determiningpair wise distances between nodes.

FIG. 1 shows an exemplary collection 10 of sensor nodes 12-23. Thesensor nodes 12-23 are distributed through a spatial region, e.g., aland surface, a bottom of a lake, or the walls of an office building.Various embodiments may have different numbers of such sensor nodes anddifferent spatial distributions of the sensor nodes.

Each sensor node 12-23 includes a sensor, S, that is configured tomeasure the local value of one or more selected external environmentalconditions. The one or more selected external environmental conditionsvary in both time and space. Examples of the selected externalenvironmental conditions may include a light intensity, a sound level, apH level, presence or absence of a cloud shadow, the nearby presence orabsence of a vehicle or a random walker such as an animal, etc.

Each sensor node 12-23 is configured to compile an associated list ofdata entries. In the individual lists, each entry is derived from alocal observation of the selected one or more external environmentalconditions by the associated node's sensor S. The lists may, e.g., bemaintained on data storage devices, D, in the associated sensor nodes12-23. That is, each node 12-23 may compile and locally store a list ofmeasured values for the one or more selected external environmentalconditions. The step of storing may optionally be performed locally on awriteable and readable data storage device, D, in the associated node12-23.

FIG. 2 illustrates one example of such a list, L. The list L is, e.g.,stored on the data storage device D of the associated sensor node 12-23.The sensor node 12-23 produces the list L in response to a sequence of Nmeasurement cycles with its sensor S. The associated sensor node 12-23may update the list L periodically to add a new entry. The list Lincludes one entry E1, E2, E3, . . . , EN for each of the N measurementtimes. Each entry E1, . . . , EN provides a measurement time and themeasured local value(s) of the one or more selected environmentalconditions at the measurement time of the entry E1, . . . , EN. Eachmeasured value may be a direct measurement of the node's sensor S, e.g.,a sky light intensity, or may be derived from a direct measurement ofthe node's sensor S. An example of a value derived from a directmeasurement is a binary value for the presence or absence of a cloudshadow at the associated sensor node. Such a value could, e.g., bederived from a light intensity measurement by the node's sensor S. Insome embodiments, the measurement times are omitted from the entries E1,. . . , EN, because the times are inherent from the sequential positionsof the entries E1, . . . , EN on the list L.

In some embodiments, the collection 10 also includes a central receiver24 that is configured to receive communications from the nodes 12-23.The central receiver 24 receives from each node 12-23 a list of thelocal measurements of the one or more selected environmental conditions,e.g., list L of FIG. 2. The central receiver 24 may, e.g., be an accesspoint for a contention neighborhood of a network.

In other embodiments, the collection 10 is a spatially distributed setof sensor nodes 12-23, wherein the sensor nodes 12-23 are not configuredto communication with such a centralized receiver 24. Instead, theindividual sensor nodes 12-23 are distributed over a spatial region,e.g., to sense and record local conditions at various positions in theregion over a fixed time period. The individual sensor nodes 12-23 may,e.g., record one or more local environmental conditions such as localtemperature, local light intensity, local sound intensity, or local pHand/or salinity at the bottom of a lake. At the end of the fixed timeperiod, the individual sensor nodes 12-23 may be collected for readoutof the measurements made. For example, sensor nodes 12-23 that recordenvironmental conditions at the bottom of a lake may be configured tofloat to the lake's surface for collection and downloading of recordedmeasurements of the environmental condition(s) at the bottom of thelake.

In some embodiments, the collection 10 of sensor nodes 12-23 isspatially distributed over a land region such that each sensor, S, isfacing skyward. In such an embodiment, each sensor node 12-23 may beconfigured to distinguish whether it is in a shadow of a cloud or is notin a shadow of a cloud. For example, each sensor node 12-23 may be ableto distinguish temporally abrupt decreases and increases in the skylight intensity seen by its sensor S. Such temporally abrupt increasesand decreases would, e.g., result from an edge of cloud passing betweenthe sensor S and the sun.

In various embodiments, it is desirable to obtain information on pairwise distances between the sensor nodes 12-23 from the localmeasurements by the sensors

In some embodiments, the sensor nodes 12-23 are anchorite nodes, i.e.,nodes that do not perform inter-node chatter.

FIG. 3 illustrates a method 30 of estimating pair wise distances betweensensor nodes of a spatially distributed collection, e.g., collection 10of FIG. 1.

The method 30 includes receiving a sequence of measurements of one ormore selected environmental conditions from each of the sensor nodes(step 32). In each sequence, the individual measurements are values ofone or more selected local environmental condition(s) as measured at oneof the sensor nodes at a sequence of times. For example, each sequencemay be a list of entries E1, . . . , EN similar to list L of FIG. 2. Ineach sequence, each individual measurement is a value of the one or moreselected environmental conditions observed at the location of thecorresponding sensor node, e.g., sensor nodes 12-23 of FIG. 1.

In the various embodiments of the method 30, each of the one or moreselected environmental conditions varies in both space and time.Exemplary selected environment conditions have been described withrespect to the collection 10 of sensor nodes 12-23 of FIG. 1. Theselected external environmental conditions may include a lightintensity, a sound level, a pH level, a salinity level, presence orabsence of a cloud shadow, nearby presence or absence of a vehicle or arandom walker such as an animal, etc. The values of measurementsreceived at the step 32 may be values of direct measurements by thenodes' sensors, e.g., measured intensities of sun light, or may bevalues derived from direct measurements by the nodes' sensors, e.g., thepresence of absence of a cloud shadow. The lists of measurements of theselected environmental condition(s) may be measured by the differentsensor nodes at the same sequence of time values or at differentsequences of time values.

The method 30 includes determining a spatial correlation between themeasurements received from two or more of the sensor nodes (step 34).The determination of the spatial correlation may, e.g., involveaveraging over all or part the temporal sequence of receivedmeasurements of one of more of the selected environmental conditions.Each local value of a selected environmental condition is described by avariable whose value depends on both time, t_(k), and location, j, i.e.,ξ=ξ_(j)(t_(k)). For such a variable ξ, the N-point spatial correlation,<ξ_(j1)gggξ_(jN)>_(N), may be, e.g., evaluated as a time average givenby:

$\left\langle {\xi_{j\; 1}{ggg}\;\xi_{jN}} \right\rangle_{N} = {K^{- 1}{\sum\limits_{p = 1}^{K}\;{{\xi_{j\; 1}\left( t_{p} \right)}{ggg}\;{{\xi_{j\; N}\left( t_{p} \right)}.}}}}$In the above-definition, the sum is over a set of times “p” at which thevariable ξ_(j)(t_(k)) has been measured. Indeed, the sum may be overpart or all of the sequence of times in the lists of measurementsreceived in the step 32. The above form of the N-point spatialcorrelation often converges to a value that is fairly insensitive to theset of times used in the temporal average. For example, convergence maybe expected if the average is over a large number, K, of times, and theindividual times t_(p) of the average are uniformly spread over a longenough time period.

Furthermore, the value of the N-point spatial correlation depends on theN spatial locations, i.e., j1, . . . jN, of the local variable, ξ,therein. For that reason, the N-point correlation provides informationon relative distances between the spatial points, i.e., j1, . . . jN,where the local variable, ξ, is measured by the N sensor nodes.

The method 30 includes estimating distances between the two or more ofthe sensor nodes based on the determined spatial correlation(s) betweenmeasurements of the one or more selected environmental conditions by thetwo or more sensor nodes (step 36). The step of estimating distancesmay, e.g., involve explicitly determining pair wise distances betweensensor nodes or may involve qualitatively determining pair wisedistances between said sensor nodes. As an example of qualitativelydetermining said pair wise distances, the estimating step may involveproducing lists of near neighbor sensor node pairs and/or lists ofwidely separated sensor node pairs.

In some embodiments of method 30, step 36 of estimating distancesbetween two or more of the sensor nodes may be performed without usingany GPS location-determinations. That is, some embodiments of step 36 donot use any GPS-derived location information on the sensor nodes whoserelative distances are determined.

Different embodiments of method 30 may use spatial correlations withdifferent numbers of points in steps 34 and 36. For example, someembodiments may use only 2-point spatial correlations at steps 34 and36. As a further example, other embodiments may use only 3-pointcorrelations at steps 34 and 36. As a yet further example, otherembodiments may use 2-point and 3-point correlations at steps 34 and 36.Finally, yet other embodiments, may use spatial correlations with morethan three points.

In various embodiments, it may be advantageous to base the method 30 ona special type of spatial correlation, i.e., the 2-point cumulant. The2-point cumulant of a local variable, ξ, which corresponds to a selectedlocal environmental condition, will be written as <ξ_(j1)ξ_(jN)>_(2-CM)and is given by:<ξ_(j1)ξ_(j2)>_(2-CM)=<ξ_(j1)ξ_(j2)>₂−<ξ_(j1)>₁·<ξ_(j2)>₁.N-point cumulants can have simple spatial properties due to a clusteringproperty that is often obeyed by spatial correlations of localvariables. According to clustering, an N-point spatial correlationshould factorize into a product of a single point spatial correlationand an (N-1)-point spatial correlation as the distance between the firstpoint and the other (N-1) points of the N-point spatial correlationbecome large. In particular, the cluster property is:

$\left\langle {\xi_{j\; 1}{ggg}\;\xi_{jN}} \right\rangle_{N}\underset{{{{{{j\; 1} - {jQ}}}\rightarrow{\infty\mspace{14mu}{for}\mspace{14mu} Q}} = 2},\ldots\mspace{14mu},N}{\rightarrow}{\left\langle \xi_{j\; 1} \right\rangle_{1}{\left\langle {{ggg}\;\xi_{j\; N}} \right\rangle_{N - 1}.}}$In light of this property, associated N-point cumulants typically havevalues that decrease as pair wise distances between the points thereinincrease, i.e., at least for large enough distances.

The 2-point cumulant, <ξ_(j1)ξ_(jN)>_(2-CM), of a local variable,ξ_(j)(t_(k)), often has further properties that make it simple to use inmaking estimations of the pair wise distances between its two spatialpoints. The 2-point cumulant is typically positive when its spatialpoints coincide, i.e., j1=j2, and thus, is typically also positive overa small range of separations of its two points. Furthermore, the clusterproperty implies that the 2-point cumulant should go to zero as its twopoints become separated by large distances. Thus, the magnitude of the2-point cumulant of a local variable, will often provide a rather directmeasure of the relative distance between its points, at least, for smallenough separations of said points.

FIGS. 4A-4E illustrate the operation of embodiments of method 30 inwhich cloud shadows are used to determine pair wise distances betweenthe sensor nodes 12-23 of FIG. 1. That is, the selected environmentalvariable is the presence or absence of a cloud shadow at a node's sensorS, i.e., a local binary variable.

FIGS. 4A-4C provide a time-lapse sequence of pictures of the motion ofthe shadow, S1, of an exemplary circular cloud that moves with velocity,

, over a region on which sensor nodes are distributed, i.e., the sensornodes 12-23 of FIG. 1. At the time of FIG. 4A, the sensor nodes 12 and13 are both in the shadow S1 and thus, will record the same value of thebinary variable associated with the presence or absence of a cloudshadow. Similarly, at the time of FIG. 4B, the sensor nodes 12 and 13are both outside of the shadow S1 and thus, will again record the samevalue of the binary variable associated with the presence or absence ofa cloud shadow. At the time of FIG. 4B, the sensor nodes 15, 18, and 19are in the shadow S1 and thus, will record the same value of the binaryvariable associated with the presence or absence of a cloud shadow. Atthe time of FIG. 4C, the sensor nodes 15, 18, and 19 are not the shadowS1 and thus, will again record the same value of the binary variableassociated with the presence or absence of a cloud shadow. At the timeof FIG. 4C, the sensor nodes 21 and 23 are in the shadow S1 and thus,will record the same value of the binary variable associated with thepresence or absence of a cloud shadow. Thus, FIGS. 4A-4C illustrate thatthe passage of the cloud shadow S1 can produce a nontrivial spatialcorrelation between the measurements of sensor nodes 12 and 13; anontrivial spatial correlation between the measurements of sensor nodes15, 18, and 19; and a nontrivial spatial correlation between themeasurements of sensor nodes 21 and 23. Indeed, such spatialcorrelations are indicative of the small pair wise distances between thesensor nodes in each of these three subsets.

FIG. 5 shows a circular shadow, S2, of a second cloud that has velocity,

, over the region on which the sensor nodes 12-23 are distributed. Theshadow S2 of the second cloud travels over a portion of the sensor nodes12-23 along a different path and thus, can generate correlations betweenthe measurements of the presence or absence of a cloud shadow betweendifferent spatially close pairs of sensor nodes 12-23. In particular,the shadow S2 may generate nontrivial spatial correlations between themeasurements of the presence or absence of a cloud by sensor nodes 16and 17, which did not detect the shadow S1 of the first cloud.

FIG. 6 shows a circular shadow, S3, of a third cloud that has avelocity,

, over the region on which the sensor nodes 12-23 are distributed. Theshadow S3 of the third cloud can generate nontrivial spatialcorrelations between the measurements of presence or absence of a cloudshadow by sensor nodes 22 and 23. Indeed, the shadow S3 is smaller thanshadows S1 and S2 so that nontrivial correlations produced by thepassage of this cloud can distinguish that the sensor nodes 22 and 23have a smaller pair wise separations that other pairs of sensor nodes,e.g., the pair of sensor nodes (16, 17).

FIGS. 4A-4C, 5, and 6 illustrate how cloud shadows of different sizesand along different paths can generate spatial correlations amongbetween measurements of the sensor nodes 12-23. These examplesillustrate that the measured 2-point cumulant of a variable for thepresence or absence of cloud shadows provides a useful measure of pairwise distances between sensor nodes in the method 30 of FIG. 3.

FIGS. 7A and 7B show the results of two simulations of 2-point cumulantsas a function of pair wise distance between the sensor nodes of a largercollection. The 2-point cumulants are spatial correlations for a localbinary variable whose value again determines whether a cloud shadow ispresent or absent. In the simulations, about 1,000 sensor nodes weredistributed with a substantially random uniform spatial distributionover the unit square, and about 1,000 time measurements of the localvariable for the presence or absence of a cloud shadow were made toevaluate the 2-point cumulants.

FIG. 7A plots results of a simulation in which cloud shadows were roundand had radii uniformly distributed in the interval [0, 0.4] as aPoisson random field with density 40. The plots show the measuredmagnitude of the 2-point cumulant of the binary variable for presence orabsence of a cloud shadow as a function of pair wise distances betweenthe sensor nodes actually measuring this binary variable. For pair wisedistances of about 0.2 or less, the simulated magnitudes of the 2-pointcumulant correlate well with the distances between the measuring sensornodes. When using the 2-point cumulant to determine these distances, thesimulation indicates an error that is roughly equal to the verticalspread in the simulation points.

FIG. 7B shows the results of a simulation in which the cloud shadowswere ½-planes bounded by lines whose orientations had an isotropicdistribution. Again, the simulation results plot the magnitude of the2-point cumulant of the binary variable for presence or absence of acloud shadow as a function of the pair wise distance between the sensornodes actually measuring the binary variable. For a large range of pairwise distances, the simulated magnitudes of the 2-point cumulantcorrelate well with the pair wise distances between the measuring sensornodes.

While the magnitude of 2-point cumulant for the variable indicatingpresence or absence of a cloud shadow correlates well with distance ineach of the simulations of FIGS. 7A and 7B. FIGS. 7A and 7B also showthat the 2-point cumulant's dependence on distance may be sensitive tothe distribution of cloud shadows used in evaluating the temporalaverage. This “ensemble” dependence may be lower if the 2-point cumulantis used to only identify close neighboring sensor nodes. Thus, in someembodiments of method 30, estimating step 36 may only use an abovethreshold magnitude of this 2-point cumulant as the indication that avery small distance separates a corresponding pair of the sensor nodes.For example, in the simulations of FIGS. 7A-7B, the estimating step 36of method 30 shown in FIG. 3 could have used a threshold magnitude ofabout 0.22 to 0.23 for the 2-point cumulant as indicating that thedistance between the corresponding pair of sensor nodes is less thanabout 0.1. In such an embodiment, the distance-estimating step 36 wouldsimply determine which pairs of sensor nodes correspond to nearneighbors.

FIG. 8 illustrates a method 40 of spatially mapping sensor nodes in aspatially distributed collection, e.g., sensor nodes 12-23 of FIG. 1.

The method 40 includes performing steps 32, 34, and 36 as described forone of the embodiments of method 30 of FIG. 3. In this embodiment, thesteps 34 and 36 include however, determining spatial correlations andestimating pair wise distances between at least three of the sensornodes. In particular, the method 40 includes forming a spatial map ofthe at least three sensor nodes based on the estimated distances betweenpairs of the sensor nodes as found at step 36 (step 48).

In some embodiments of the method 40, step 48 produces a spatial map inthe form of a connectivity pattern for the sensor nodes. Such a patternsshow, e.g., how many hops between near neighbor sensor nodes are neededto go between a pair of sensor nodes. That is, such a map could simplyindicate which pairs of nodes are physically close to each other.

In other embodiments of the method 40, step 48 produces a spatial map ofthe physical locations of the sensor nodes, i.e., based on estimates ofactual physical distances as derived from the pair wise separations ofthe sensor nodes. Indeed, algorithms and methods that use triangulationand/or angular separation algorithms for making such maps are known forconstructing such physical spatial maps from estimates of the physicalpair wise separations of the points being mapped. Examples of suchalgorithms are described in one or more of “Locating the Nodes” by NealPatwari et al, IEEE Signal Processing Magazine (July 2005) pages 54-69;“Ad hoc positioning system (APS)” by Dragos Niculescu et al, GLOBECOM2001-IEEE Global Telecommunications Conference, no. 1, November 2001pages 2926-2931; published U.S. Patent Application No. 20030128355 A1 ofNeal Patwari et al; and published U.S. Patent Application No.20030130793 A1 of Neal Patwari et al. The two above-listed articles andtwo above-listed published U.S. patent applications are incorporatedherein by reference in their entirety. The step 48 of method 40 may useone of the above-described methods.

In some embodiments of method 40, step 48 produces a spatial map of thesensor nodes of a collection based, in part, on one or a few absolutelocation-determinations. Indeed, in some embodiments, one or a few ofthe sensor nodes have a GPS transponder that is used to absolutelylocate the corresponding sensor node. Then, the step 48 uses theabsolute locations of the one or a few sensor nodes and the pair wisedistances of sensor nodes as obtained at step 36 to estimate theabsolute locations of the entire collection of sensor nodes.

FIG. 9 illustrates an exemplary hardware device 50 for implementingvarious embodiments of above-described methods 30 and 40 of FIGS. 3 and8. For example, the hardware device 50 may be located in centralreceiver 24 of FIG. 1.

The hardware device 50 includes a conventional digital processor 52; arandom access memory 54; a program storage medium 56, e.g., a magneticor optical disk, read-only memory, or a hard drive; and one or moreinternal digital data buses 58. The hardware device 50 also includes oneor more communication interfaces 60 for receiving the lists of temporalsequences of locally measured values for one or more selectedenvironmental conditions, e.g., lists L of FIG. 2, from the measuringsensor nodes, e.g., sensor nodes 12-23 of FIG. 1. The communicationinterface 60 may, e.g., be a wireless communication interface configuredto receive transmissions of said lists from the individual sensor nodesor from a subset of said sensor nodes. Alternatively, the communicationinterface 60 may, e.g., be a keyboard or other interface for receivingsaid lists of measurements from the sensor nodes. In this laterembodiment, the lists may be collected from the sensor nodes by anoperator who then, uses the interface 60 to manually transmit the liststo the hardware device 50 for further processing according toabove-described method 30 or 40. The program storage medium 56 and/orthe random access memory 54 store a program of instructions forperforming the method 30 or 40. The instructions of the program arestored in a form executable on the digital processor 52.

From the above disclosure, the figures, and the claims, otherembodiments will be apparent to those of skill in the art.

What I claim is:
 1. A data storage medium encoding a machine-executableor digital processor-executable program, the program including asequence of instructions for performing a method, the method comprising:receiving a plurality of temporal sequences of measurements of aselected local environmental condition, each sequence of measurementsbeing made by a corresponding sensor node; determining an amount ofcorrelation between the sequences of measurements of the selected localenvironmental condition received from two or more of the sensor nodes;and estimating a distance between the two or more of the sensor nodesbased on the determined amount of correlation.
 2. The medium of claim 1,wherein the correlation is a spatial correlation between themeasurements from the two or more of the nodes.
 3. The medium of claim1, wherein each of the received measurements has a time stamprepresenting the time of the corresponding one of the measurements. 4.The medium of claim 1, wherein the step of determining is made withoutprocessing a communication between the two or more of the sensor nodes.5. The medium of claim 1, wherein the receiving includes processingcommunications received from mobile devices, each communication havingone of the sequences, one of the mobile devices corresponding to each ofthe sequences.
 6. The medium of claim 1, wherein the receiving includesprocessing communications received from spatially fixed nodes, eachcommunication having one of the sequences, one of the spatially fixednodes corresponding to each of the sequences.
 7. The medium of claim 1,wherein the steps of determining and estimating are performed withoutusing GPS location-determinations of any of the two or more of thesensor nodes.
 8. The medium of claim 1, the method further comprising:making a map to represent spatial locations of more than two of thesensor nodes based on the estimated one or more distances between atleast three of the sensor nodes.
 9. The medium of claim 1, wherein thestep of determining includes determining a 2-point cumulant between twoof the sensor nodes.